Dynamics: Energy Exchange

Dropping a series of balls

This model gives an entertaining demonstration of conservation of energy.

Fig. 13-4: Dropping a series of balls

Fig. 13-4 shows four rubber balls of different sizes placed together using a plastic bar passing through their centres with the smaller balls resting on the larger balls.

When the balls are lifted vertically for a distance of about 0.15 m from a desk and then released, the smallest ball rebounds to hit the ceiling which is over two metres above the desk. This observation can be explained using either the principle of conservation of energy or the princile of conservation of momentum.

The total mass of the four balls is 120 grams and the mass of the smallest ball is 5 grams. The gravitation potential energy of the balls before dropping them is estimated to be:

After the impact of the largest ball on the desk, the three larger balls bounce up almost together about 0.03m. According to the conservation of energy, the total gravitational potential energy before and after impact should be the same if no energy loss takes place, i.e.

From the above equation, the predicted bounce height of the smallest ball is 2.92m. Actually there is some loss of energy due to the impacts between the largest ball and the desk and between the adjacent balls, so the smallest ball would not bounce quite as high as 2.92 m.

This example can also be analysed using the principle of conservation of momentum.